Transcript Goldenson Center Lifetime Financial Planning Model

2015 Goldenson Center
Advisory Board Meeting
Goldenson Center
Unleashing the creative
potential
Jay Vadiveloo, Director of the Goldenson Center
Deborah Howard, Marketing & Communications Advisor
Cassandra Fibbe, Marketing & Communications Advisor
5
Deborah Howard
Marketing and Communications Advisor
Human Productivity
How to maximize individual
and group creativity
1. Complete freedom in thinking is
necessary to unleash the Creative
Process
How to maximize individual
and group creativity
2. Students are the best resources to
utilize for projects requiring creative
thinking
How to maximize individual
and group creativity
3. Students adapt and learn quickly from
one another
How to maximize individual
and group creativity
4. Students are extremely responsible
when they are given total ownership of a
project
How to maximize individual
and group creativity
5. Students are naturally self-governing
as a group
How to maximize individual
and group creativity
6. Once all of the above ideas are
incorporated, work becomes a totally
fun and gratifying exercise.
Project Challenges
“Be careful what you wish for”
Cassandra Fibbe
Marketing and Communications Advisor
How does the Goldenson
Center transform young,
inexperienced students into
a group capable of tackling
these huge projects?
Goldenson Center Philosophy

Team of Students
P
Goldenson Center Philosophy

Overstaffed team of students
Goldenson Center Philosophy

Fixed stipend independent of the
number of hours worked
Goldenson Center Philosophy

See the project from start to finish
Goldenson Center Philosophy

Weekly client meetings
Goldenson Center Philosophy

Face to face client presentations
How did these steps
maximize individual and
group creativity?
Student Perspective
 Complete freedom in thinking
 Opportunity to do real-life work with
fellow classmates
 Challenging out-of-the-box thinking
 Project ownership and responsibility
 Work becomes a fun and totally
gratifying experience
Director Perspective
“I consider myself akin to the conductor
of an orchestra of potentially talented
but amateur musicians. The players
start off unable to perform any music,
and my role is to ensure that at the end
of the project, the orchestra will be
able to perform a symphony that
captivates the audience”
- Jay Vadiveloo
Contact information
Jay Vadiveloo, Director of the Goldenson Center,
[email protected]
Deborah Howard, Marketing & Communications Advisor,
[email protected]
Cassandra Fibbe, Marketing & Communications Advisor,
[email protected]
Longevity Risk Analysis
for Pension Liabilities
9-11-2015
Tian Xia and Jichao He
Goldenson Center for Actuarial Research
University of Connecticut
Agenda
1.
Motivation and Introduction
2.
Pure Collar Mortality Table extracted from RP2014
3.
IAM2012 to RP2014 Wearing off effect
4.
Conclusions
1
Motivation and Introduction


How to use SOA Blue Collar/White Collar mortality tables on individuals?

SOA produced collar-based RP2014 with mixed blue and white collars at industry level.

Solution:

Make proper assumptions on blue/white collar proportions

Discover the proportions of male/female based on third-party data (HRS)

Generate a set of formulas to calculate pure mortalities given blended mortalities

Create spreadsheets to apply the formulas on SOA tables
Is the mortality different for a 70 year old who selects a life income at age 70
versus for a 70 year old who selected a life income 5 years earlier?

Yes, the one selected 5 years earlier (65) has a higher mortality rate at 70. The impact of
selection of a participant choosing lifetime income over a lump sum wears off over time.

Solution:

Justify our answer with third-party data (HRS)

Use select-ultimate approach and GLM to quantify the wear-off effect

Extrapolate our findings on SOA mortality tables based on some assumptions
2
Background on HRS
The Health and Retirement Study (HRS) is a longitudinal study conducted by the
University of Michigan, and funded by the National Institute on Aging. This study
collected health and retirement data of about 37,000 individuals over 2 decades.
We select HRS for this study based on the following reasons:

HRS has detailed information of participants’ pension plans, individual life
annuities, etc.

Industry category and occupation are available for participants in HRS.

Age of retirement is recorded for every job of individuals, which is critical for
wear-off duration calculation.

The study captured 11409 deaths during 20 years, making it an ideal database
for mortality rate research.
3
Process to Derive Pure Collar Mortality
Table

Same as “Male and Female Mortality Tables => Unisex Mortality Table”

Blended Blue and White Collar Mortality Table => Pure Blue and White Collar
Mortality Table
Questions:

Blended Proportion

Starting Age
4
Assumptions – Blended Proportion

RP2014 classifies a group as blue-collar if at least 70% of workers are blue
collar. Same for white collar classification i.e. BC and WC mortality tables in
RP2014 are really blended mortality tables

We assume the proportion of pure white collar in blended blue collar is 15%,
same for the pure blue collar in blended white collar.

Aggregate proportion in Blended Blue Collar Table: 15% WC- 85% BC

Aggregate proportion in Blended White Collar Table: 15% BC- 85% WC
5
Assumptions – Blended Proportion

Distribution Summary (Based on HRS data)
Blended Blue Collar
(White Collar % - Blue Collar %)
Blended White Collar
(Blue Collar % - White Collar %)
Aggregate
15% - 85%
15% - 85%
Male
10% - 90%
21% - 79%
Female
21% - 79%
11% - 89%
6
Formula - forward

The forward formula is created to calculate the older age pure collar
mortalities.
q
q
W
x
B
x
W
x
r
B
x
r
qWx
qWx  rxW qxB  (1  rxW )qWx
q xB
qxB  (1  rxB )qxB  rxB qWx
W
x 1
r
B
x 1
r
q
B
x +1
qWx+1
q
B
x +1
qWx1
rxW1 
B
x 1
r

rxW (1  qxB )
1  qWx
rxB (1  qWx )
1  qxB
7
Formula - Backward

The backward formula is created to calculate the younger age pure collar
mortalities.
qWx-1
qxB-1
B
x
r
W
x
r
qxB-1
W
qx -1
qxB1  (1  rxB1 )qxB1  rxB1qWx1
qWx1  rxW1qxB1  (1  rxW1 )qWx1
B
x -1
r
W
x -1
r
W
x -2
q
B
x -2
q
rxW 
q
W
x -2
q
B
x -2
rxB 
rxW1 (1  qxB1 )
1  qWx
rxB1 (1  qWx 1 )
1  qxB1
8
Pure Mortality Tables
Pure Mortality of Males
Pure Mortality of Females
0.35
0.30
0.30
0.25
0.25
0.20
0.20
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0.00
50 53 56 59 62 65 68 71 74 77 80 83 86 89 92 95 98
50 53 56 59 62 65 68 71 74 77 80 83 86 89 92 95 98
Pure Mortality of Blue-collar
Pure Mortality of Blue-collar
Pure Mortality of White-collar
Pure Mortality of White-collar
9
Annuity Due N.S.P. for Males – Blended
BC vs. Pure BC
10
Annuity Due N.S.P. for Males – Blended
WC vs. Pure WC
11
RP2014 vs IAM2012 mortality differences

IAM2012 mortality chosen for individuals who selected a life annuity when
they had a lump sum option

RP2014 mortality is chosen for individuals who have a life annuity but never
had a lump sum option

IAM2012 has better mortality

Introduce the select and ultimate approach


IAM2012 – select mortality for annuitants with a lump sum option

RP2014 – ultimate mortality to capture the wearing-off effect of the lower
mortality of annuitants with a lump sum option
How to create the select and ultimate table with selection periods

Generalized linear model (GLM) – Accelerated Life Model

Fitted GLM model converted to mortality table
12
Framework of Wear-off Effect Analysis
IAM2012 and RP2014
Mortality Tables
Find data with
subjects similar
to SOA study
External Database
(HRS)
Take appropriate
subsets from
external database
Fit GLM to relate
wear-off duration
and mortality rate
Select Tables Based on
IAM2012 and RP2014
Generalize select
and ultimate table
under assumptions
Obtain mortality w/
duration variation
incorporated
Use select and
ultimate strategy
to get period
Mortality Tables
Produced from GLM
13
GLM: Results
HRS Select and "Ultimate" Mortality (Male, Period=7)
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
q[70-1]+1
q[70-5]+5
q[70-2]+2
q[70-6]+6
q[70-3]+3
q[70-7]+7
q[70-4]+4
q70
14
GLM: Results
HRS Select and "Ultimate" Mortality (Female, Period = 10)
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
q[70-2]+2+t
q[70-8]+8+t
q[70-4]+4+t
q[70-10]+10+t
q[70-6]+6+t
q70+t
15
Wear-off Modifications on IAM/RP
HRS Period and Duration Modification Applied on
RP2014 and IAM2012 (Male, D=7)
0.3
0.25
0.2
0.15
0.1
0.05
0
70
72
74
76
78
RP2014
Duration=3
80
82
84
IAM2012
Duration=4
86
88
Duration=1
Duration=5
90
92
94
Duration=2
Duration=6
96
98 100
16
Wear-off Modifications on IAM/RP
HRS Period and Duration Modification Applied on
RP2014 and IAM2012 (Female, D=10)
0.25
0.2
0.15
0.1
0.05
0
70
72
RP2014
74
76
IAM2012
78
80
82
Duration=2
84
86
88
Duration=4
90
92
94
Duration=6
96
98 100
Duration=8 17
Conclusions
1.
That generating pure BC and WC mortality has implications on valuing
pensions liabilities.
2.
The GLM model captures the wearing off effect of select mortality for
retirees selecting a life annuity when they were provided a lump-sum
option, and the ultimate mortality of retirees who elected a life
annuity with no lump-sum option.
3.
In both cases, we had to use external data from HRS to supplement
the SOA published mortality studies.
18
Questions
19
Lifetime Individual Financial
Planning Model
Jiatian (Justin) Xu, Xiaoying (Sunny) Shen
Goldenson Center for Actuarial Research
2015 Goldenson Center Advisory Board Meeting
September 11 2015
Content

1. Motivation Behind Model

2. Uniqueness of Model

3. Model Design


3.1 Objective

3.2 Two - Stage Cash flow Model

3.3 MC – MC Process

3.4 Pre – Retirement Modeling

3.5 Post – Retirement Modeling

3.6 MC – MC Model to Analytical Model

3.7 Example of Inputs and Outputs
4. Conclusion
1. Motivation Behind Model

1.1 Such a model does not exist currently


Separate models exist for pre and post retirement financial planning but there is no
model that maximizes financial sustainability from current working age until death
1.2 The importance of having a financial plan that applies throughout the
lifetime of an individual is driven by several factors:

The gradual transformation of the extended family structure in the US towards a
nuclear family system and the increase in single parent households

The shifting of responsibility for guaranteeing financial security from the
government and employers to the individual

Increased uncertainty about job security and the state of the economy in general

Medical advances which are capable of prolonging retirement life, but exacerbate
the longevity risk of outliving one’s investments

Health care affordability especially for prolonged illnesses during retirement life
1. Motivation Behind Model

1.3 Lifetime financial planning is necessary since pre-retirement and postretirement risks are different and insurance products to help mitigate these
risks are different as well
Pre-Retirement
Post-Retirement
Risk
Product
Risk
Product
Premature Death
Term Life & Whole Life
Insurance
Longevity Risk of Outliving
Retirement Assets
Immediate Annuities &
Deferred Annuities
Disability
Disability Insurance
Healthcare Costs
Health Insurance
Prolonged Illness
Long Term Care
Insufficient Assets for
Retirement
Investment Portfolios
Bequest Needs
Whole Life Insurance
Investments Portfolios
2. Uniqueness of Model

2.1 Dynamic Predictive Model


Project annual cash flows to determine financial sustainability
2.2 Monte Carlo – Markov Chain (MC-MC) techniques

Annual cash flows are generated stochastically by MC-MC process

Monte Carlo simulation

distribution of annual cash flows

ruin probabilities & assets shortfalls
Markov Chain technique
transition probabilities
(healthy, disabled and dead)
2. Uniqueness of Model

2.3 Individual Financial Wellness Index (IFWI)

It quantifies individual financial sustainability on a scale of 0 to 100 by
calculating a pre-retirement Individual Financial Wellness Index (PreIFWI) and an integrated lifetime Individual Financial Wellness Index
(Integrated-IFWI)

The higher the IFWI, the greater the level of financial sustainability

The IFWI is impacted by level of financial dependencies and other
individual characteristics
3. Model Design
3.1 Objective
To maximize individual financial adequacy by providing
optimal allocation of budget
Customer
Information
•
•
•
•
•
•
•
Age
Salary
Marital
Status
Mortgage
Status
Dependent
Household
Income
…
Lifetime Individual
Financial Planning Model
(MC-MC)
Optimal
Allocation of
Budget
IFWI
3. Model Design
3.2 Two – stage Cash Flow Model
•
•
•
•
•
Health Insurance
Term Insurance
Disability Income
Whole Life Insurance
Investment Products
Pre-retirement
Optimization
Post-retirement
Optimization
Integrated
Lifetime
Financial
Planning
•
•
•
•
•
Long-term Care
Immediate Annuity
Deferred Annuity
Investment Products
Whole Life Insurance
3. Model Design
3.3 MC - MC Process


Monte-Carlo simulation
is used to provide a
distribution of cash
flows generated from
the Markov Chain
transition probabilities;
The optimization is
based on the risk
measures which are
calculated from the
statistics of the
simulated distribution
Random Paths
Ruin Prob.
Short-fall
Amount
Ending Assets
• Each path stands for a random realization of
individual’s financial status;
• Taking all the paths into consideration, we
have a profound understanding of
individual’s future financial needs.
3. Model Design
3.3 MC- MC Process
Monte Carlo Simulation Cash Flow
Markov Chain (Transition Matrix)
Female,
Age=45
Healthy
Disabled
Dead
Healthy
99.48%
0.33%
0.19%
Disabled
2.60%
94.30%
3.10%
Dead
0%
0%
100%
3. Model Design

3.4 Pre – retirement Modeling

Start from an ideal budget and an optimal allocation of the ideal budget

Ideal budget is a benchmark which represent that Pre-IFWI equals 100

Marginal Approach: unique method to get the optimal allocation of the actual budget for pre stage
An Ideal budget
and ideal optimal
allocation
MC-MC Process
Marginal Approach
The actual budget
and the actual
optimal allocation
Ideal
Accumulated
Assets
Actual Optimal
Accumulated
Assets
The actual budget
and the naive
strategy
(100% of budget
on investment
products)
3. Model Design
3.5 Post – retirement Modeling
Get initial assets from pre stage and then repeat
this process until the ruin probability to be under
some confidence level (e.g. 5%)
Ideal
Accumulated
Assets from Pre
Actual Optimal
Accumulated
Assets from Pre
Put a% of initial assets
on investment.
calculate the ruin probability at
death
use remaining actual
assets to purchase SPIA
Investment will give an
annual income b until
life expectancy
solve for the N.S.P for a
LE-deferred life annuity
providing annual income
b
Example Using 50% Investment Strategy
Total savings after LTC & Whole life
$ 500,000
Investment
$ 250,000
SPIA ( LE-deferred )
$ 100,000
SPIA ( Immediate)
$ 150,000
Annual income from investment
Annual income from SPIA ( LE-deferred )
Annual income from SPIA(Immediate)
Total retirement income
Ruin probability at death
$ 13,000
$ 13,000
$ 8,000
$ 21,000
15%
3. Model Design
3.6 MC – MC Model to Analytical Model

The MC-MC model is a highly complex stochastic
model and the optimization process takes time

Need to create an analytical (i.e. formula based)
solution which closely approximates the MC-MC
results

A generalized linear model is fitted to reproduce MC-MC
results of representative model points

The model points provide a sufficient representation of
various combinations of financial dependencies and
individual characteristics.

Statistical tests are performed to ensure a suitable fit
between the GLM results and the MC-MC output
MC-MC
Model
Analytical
Model
3. Model Design
3.7 Example of Inputs and Outputs
4. Conclusion

4.1 Financial planning is a lifetime responsibility that continues through
retirement life

4.2 Our Individual Lifetime Financial Planning model incorporates the following:


Optimal allocation of pre and post retirement insurance and investment products

Financial dependencies of individual

Evaluation of living needs of individual and estimation of affordable budget available for
financial planning

An actuarially rigorous stochastic model that determines the optimal financial planning
strategy recognizing risks of disability, death, longevity and prolonged illness

An Individual Financial Wellness Index (IFWI) that evaluates individual financial
sustainability on a scale of 1 to 100
4.3 Only individual financial planning model that incorporates both pre and post
retirement financial risks and determines the optimal lifetime financial planning
strategy
Thank You!
Questions?
Goldenson Center for Actuarial
Research
By Boyang Wang and Fan Wu
09/11/2015
Table of Contents
1. Background
 2. Model Incentive
 3. Model Description
 4. Assumptions
 5. Results
 6. Conclusions

1
Background (The phenomenon)

There are indications which suggests that more employees delay retirement
nowadays
 56% of 65 or older age population held full-time positions in 2007, up from
44% in 1995.3
 The average retirement age is 64 for men and 62 for women in last decade.1
However, given the trends in place, this will very likely change – about
60% of surveyed employees intend to retire at age 65 or older.2
*Sources:
1. Center for Retirement Research at Boston College, “The Average Retirement Age – An Update,” March 2015.
2. Gallup Poll.
3. Center for Disease Control, “Older Employees in the Workplace”, July 2012.
2
Background (Reasons)

Employees may delay retirement for various reasons
 Increasing expected lifespans mean more years in retirement that
need to be funded.
 Fewer employees are covered by DB plans.
 Financial uncertainty and lack of financial planning for
retirement by employees.
 Retiree medical programs are rare.
3
Background (Implications)

Delayed retirements have many implications
 Increasing Operating costs
 Increasing Pension/Retirement costs
 Increasing Costs of plan benefits
4
Model Incentive


Therefore, our model is developed to show employers how much aggregate
employer costs vary based on different average retirement ages.
Show the connection over serval years.
5
Model Description
 Simple,
yet realistic and reflective of a typical workplace.
 It has a user-friendly interface.
 The output is easy to understand.
 It projects aggregate employer costs.
6
Model Description-Cont’d
 It
captures all financial costs faced by an
employer.
 Model
projection is stochastic to
recognize turnover, death and retirement.
 The
model is designed in Excel with
VBA coding.
7
Model Assumptions (Age Distribution and
Average Salary)
Employee distribution and Salary
number of employees
Age
Group
100
Percentage
Number of Employees
less to 29
21%
21
30-39
22%
22
40-49
23%
23
50-59
20%
20
60 and over
14%
14
100%
100
Total
Average Salary
$25,428
$31,460
$46,592
$48,100
$63,398
Source: "Employed Persons by Detailed Industry and Age,
2013 Annual Averages." U.S. Bureau of Labor Statistics. Web.
8
Assumptions(Wage and Benefits Growth
Rate)
Wages and Salaries Growth Rate
2.8%
Benefits Growth Rate
2.6%
Source: "WAGES AND SALARIES (NOT SEASONALLY
ADJUSTED): Employment Cost Index for Wages and Salaries,
for Private Industry Workers, by Occupational Group and
Industry." U.S. Bureau of Labor Statistics. Web.
9
Model Assumptions (Ancillary Expenses Rate)
Retirement and Savings (401K)
Defined Benefit
6.63%
3.63%
Defined Contribution
3.00%
Paid Leave
9.87%
Legally Required Benefits
Social Security and Medicare (FICA)
12.23%
8.19%
Social Security
6.54%
Medicare
1.65%
Federal Unemployment Insurance
0.25%
State Unemployment Insurance
1.05%
Workers' Compensation
2.74%
4.09%
Supplemental Pay
Vacation
5.06%
Overtime and Premium
1.01%
Holiday
3.08%
Shift Differentials
0.21%
Sick
1.35%
Nonproduction Bonuses
2.87%
Personal
0.38%
Insurance
Life
11.65%
0.17%
Health
11.18%
Short-term Disability
0.13%
Long-term Disability
0.17%
Total Ancilliary Benefits
44.47%
Source: EMPLOYER COSTS FOR EMPLOYEE COMPENSATION – MARCH 2015 report
by BLS Table 7. Employer costs per hour worked for employee salary and costs as a percent of
total salary: Private industry workers, by new England region, March 2015
10
User interface
11
Result(Total Cost Index)
We just set up year 0 as the base line.
The index= current aggregate employer
costs/ aggregate employer costs in year 0
12
Other Detailed Output Results
 Total Employer Cost is broken down into three categories:
1. Costs from persisting employees.
2. Costs from employees who turnover by
death.
3. Costs from employees who retire.
 Cost indices for ancillary benefits.
quitting or
13
Conclusions
 Modeling
and projecting aggregate employer costs is a
complex process.
 Delay in the average age at retirement has a significant
impact on aggregate employer costs.
 Individual employee financial planning could be a means to
ensure employees can retire at targeted /desired retirement
ages: This could be a way to better manage aggregate
employer costs over time.
14
15
Agent Based Queuing
Model to Optimize Call
Center Agent Allocation
Gao Niu and Xiaoyu Zheng
University of Connecticut
Goldenson Center for Actuarial Research
Table of Contents
1.
Background
2.
Motivation
3.
Components in the Model
4.
Simulation Model
5.
Model Optimization
6.
Conclusion
1
1. Background
With a heavy snow in the winter, we anticipate call center will receive 50%
more calls for reporting claims. How many people do we need to keep the
total customers’ waiting time in a normal level?
Build a quantitative relationship between number of professionals and
customers’ waiting time.
2
1.1 Business Goal
Best
Customer
experience
Control
Customers’
waiting
time
Optimal
staffing level
Manage Call
Center
Expenses
2. Motivation

A fortune 500 insurance company has engaged the University of
Connecticut Goldenson Center to develop a staffing optimization
model for two of their call centers A and B.

Optimal staffing levels vary by:


different call centers

each hour during the day

each day of the week
Optimality criteria based on service levels:

For call center A, we require average waiting time to be less than 60
seconds with 70% probability.

For call center B, we require average waiting time to be less that 40
seconds with 80% probability.
4
All incoming calls are
picked up within 60
seconds
2.1 Motivation - Example
Busy
Service Level at 60 seconds = probability (incoming calls have been handled within 60 seconds)
Desired service level for CLA is 70%.
5
2.2 Motivation – Optimization Result
Too Many Staff
Working
Need more staff to
improve service level
6
2.3 Motivation – What if optimized
Time
current staff level
optimal staff level
Total
753
739
Optimization is not simply
increasing staff; it is
strategic resource
management.
Time
8:00 AM 9:00 AM 10:00 AM 11:00 AM 12:00 PM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM 7:00 PM
current staff level
40
58
71
84
74
77
78
79
80
58
34
20
optimal staff level
28
55
73
81
79
76
76
76
74
56
40
25
7
Components in the Model
Number of incoming calls
(Poisson)
Monte Carlo Queuing Simulation
model
Call length
(Log Normal)
Abandonment rate
(Linear Regression)
Number of
Professionals
Adjustable inputs
Estimated customers’
waiting time
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑙𝑙𝑠 [𝑊𝑎𝑖𝑡
𝑇𝑖𝑚𝑒 ≤ 𝑇
Evaluation
Optimization
Service
Level
N
𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝑙𝑒𝑣𝑒𝑙 𝑎𝑡 𝑇 𝑠𝑒𝑐𝑜𝑛𝑑𝑠criteria
=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐻𝑎𝑛𝑑𝑙𝑒𝑑model
𝐶𝑎𝑙𝑙𝑠
Y
Optimal staffing
level
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4. Simulation Model
Initial Stage
After 1 min
After 2 min
After 3 min
Professional 1
0
0
6
0
5
Professional 2
0
5
4
3
Professional 3
0
3
2
1+4
1
1 min waiting time
# Calls
0
2
1
1
Call length 1
3
6
4
Call length 2
5
9
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5. Model Optimization

The optimization process will find a staff allocation plan
so that the desired service level will be satisfied.

If the staff allocation plan meets the desired service level
for each hour in a day, then we can consider it as an
optimal plan.

We build an algorithm into our model so that the
optimized staffing levels can be estimated quickly and
accurately.
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5.1 Model Optimization – Efficiency Measures


The efficiency measures are the following:

Service level at 60 seconds for Call Center A is 70%

Service level at 40 seconds for Call Center B is 80%
We set a margin for the result, which means only if the
service level falls within the desired service level plus or
minus the margin, then we consider the staff allocation as
an optimal solution.

For example for Call Center A we set:
Margin = 2%, Interval = (68%, 72%).
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5.2 Model Optimization – Core Function

Opti_Full(Division=“Center A”,BeginTime=8,EndTime=19,
Criteria=“Rat_Serv_60”,Target=0.7,Margin=0.02, OptNumIte=100)
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5.3 Model Optimization – Bisection Method

For example, if the desired service level at 60 seconds is 68% to 72%, and our
current staff level is 70.
Optimal Staff Level

Then 79 is the optimal solution for this particular hour since 71% is within the
68% to 72% threshold.
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5.4 Model Optimization – Stepwise Method

Stepwise method increases or decreases number of staff by 1 unit every time.

Once we have the preliminary optimization result based on Bisection method (100
times iteration). We will apply a stepwise method (1000 times iteration) to get
the more refined optimization staff level.

If we apply bisection method with 1000 iterations, it will generate similar results
with combination of bisection and stepwise, but the process will take a long time
to be optimized.

Bisection method is for efficiency.

Stepwise method is for accuracy.
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5.5 Model Optimization – Results for Center A
Data are based on Monday, first quarter 2015, Center A.
 We are setting the target for service level at 70% with a 2% margin. If the
service level falls between 68% and 72%, then we consider the staff
allocation as an optimal solution.
 With a calibrated model; by the combination of bisection method and
stepwise method, optimization results are as the following:

Time
current staff level
optimal staff level
Total
753
739
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Conclusion



Call center staff optimization is not your typical actuarial science research
project:

Needed a team of statistics and actuarial science students to develop the model.

A good example of a multidisciplinary approach to solving complex actuarial
problems
Call center staff optimization is an example of strategic resource
management and the model we developed helps a company:

Improve efficiency standards

Reduce overall staffing needs
Our modeling technique can be applied to analyze and optimize any customer
service operation
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Our Model could also be Used Here
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Thank you!
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